In the end I talked to LG tech support and they assured me that Reset to Initial Settings would not delete the Netflix app, so I did. Initially it appeared it had deleted the Netflix app, but I suspect it may have reappeared after a while or after a further restart, but in any event, yes it did fix the issues with the store so I was able to re-download the Netflix app and other apps.
I wish there was a way to “back up” your TV, but given there isn't, resetting seems to work if you're brave enough to try it.